python - Numpy/Scipy 八函数的结果不一致

Question

我从 scipy.linalg.eigh 函数得到不一致的结果(如果我尝试使用 numpy.linalg.eigh )。即使我使用相同的输入，得到的值也是不同的。为了以防万一，我尝试将随机种子设置为常量，但仍然没有成功。

这是我的测试代码:

print('#'*50)

import numpy as np
import scipy
from scipy.linalg import eigh

# Make a random symmetric matrix
m_size = 1500
A = scipy.random.rand(m_size, m_size)
L = np.triu(A) + np.triu(A,1).T
# Verify that matrix is symmetric
print('L symmetric: %s' % np.array_equal(L,L.T))
print('')

# Just to make sure that changes to one L won't effect changes to another
# and that we are starting with the exact same input.
import copy
L1 = copy.deepcopy(L)
L2 = copy.deepcopy(L)
L3 = copy.deepcopy(L)
L4 = copy.deepcopy(L)
L5 = copy.deepcopy(L)

# Sanity check that inputs are the same
print('L == L1 (before): %s' % str(np.array_equal(L,L1)))
print('L == L2 (before): %s' % str(np.array_equal(L,L2)))
print('L == L3 (before): %s' % str(np.array_equal(L,L3)))
print('L == L4 (before): %s' % str(np.array_equal(L,L4)))
print('L == L5 (before): %s' % str(np.array_equal(L,L5)))
print('L1 == L2 (before): %s' % str(np.array_equal(L1,L2)))
print('L1 == L3 (before): %s' % str(np.array_equal(L1,L3)))
print('L1 == L4 (before): %s' % str(np.array_equal(L1,L4)))
print('L1 == L5 (before): %s' % str(np.array_equal(L1,L5)))
print('L2 == L3 (before): %s' % str(np.array_equal(L2,L3)))
print('L2 == L4 (before): %s' % str(np.array_equal(L2,L4)))
print('L2 == L5 (before): %s' % str(np.array_equal(L2,L5)))
print('L3 == L4 (before): %s' % str(np.array_equal(L3,L4)))
print('L3 == L5 (before): %s' % str(np.array_equal(L3,L5)))
print('L4 == L5 (before): %s' % str(np.array_equal(L4,L5)))
print('')

# Normally, only np.random.seed(5) should set the random generator for both
# numpy and scipy functions, but just in case, I've included both here
np.random.seed(5)
scipy.random.seed(5)
[eigval,U] = eigh(L,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval1,U1] = eigh(L1,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval2,U2] = eigh(L2,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval3,U3] = eigh(L3,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval4,U4] = eigh(L4,eigvals=(0,1))

np.random.seed(5)
scipy.random.seed(5)
[eigval5,U5] = eigh(L5,eigvals=(0,1))

# Make sure the inputs still match each other after the function
print('L == L1 (after): %s' % str(np.array_equal(L,L1)))
print('L == L2 (after): %s' % str(np.array_equal(L,L2)))
print('L == L3 (after): %s' % str(np.array_equal(L,L3)))
print('L == L4 (after): %s' % str(np.array_equal(L,L4)))
print('L == L5 (after): %s' % str(np.array_equal(L,L5)))
print('L1 == L2 (after): %s' % str(np.array_equal(L1,L2)))
print('L1 == L3 (after): %s' % str(np.array_equal(L1,L3)))
print('L1 == L4 (after): %s' % str(np.array_equal(L1,L4)))
print('L1 == L5 (after): %s' % str(np.array_equal(L1,L5)))
print('L2 == L3 (after): %s' % str(np.array_equal(L2,L3)))
print('L2 == L4 (after): %s' % str(np.array_equal(L2,L4)))
print('L2 == L5 (after): %s' % str(np.array_equal(L2,L5)))
print('L3 == L4 (after): %s' % str(np.array_equal(L3,L4)))
print('L3 == L5 (after): %s' % str(np.array_equal(L3,L5)))
print('L4 == L5 (after): %s' % str(np.array_equal(L4,L5)))
print('')

# Check to see if the outputs match each other
print('U == U1: %s' % str(np.array_equal(U,U1)))
print('U == U2: %s' % str(np.array_equal(U,U2)))
print('U == U3: %s' % str(np.array_equal(U,U3)))
print('U == U4: %s' % str(np.array_equal(U,U4)))
print('U == U5: %s' % str(np.array_equal(U,U5)))
print('U1 == U2: %s' % str(np.array_equal(U1,U2)))
print('U1 == U3: %s' % str(np.array_equal(U1,U3)))
print('U1 == U4: %s' % str(np.array_equal(U1,U4)))
print('U1 == U5: %s' % str(np.array_equal(U1,U5)))
print('U2 == U3: %s' % str(np.array_equal(U2,U3)))
print('U2 == U4: %s' % str(np.array_equal(U2,U4)))
print('U2 == U5: %s' % str(np.array_equal(U2,U5)))
print('U3 == U4: %s' % str(np.array_equal(U3,U4)))
print('U3 == U5: %s' % str(np.array_equal(U3,U5)))
print('U4 == U5: %s' % str(np.array_equal(U4,U5)))
print('')
print('eigval == eigval1: %s' % str(np.array_equal(eigval,eigval1)))
print('eigval == eigval2: %s' % str(np.array_equal(eigval,eigval2)))
print('eigval == eigval3: %s' % str(np.array_equal(eigval,eigval3)))
print('eigval == eigval4: %s' % str(np.array_equal(eigval,eigval4)))
print('eigval == eigval5: %s' % str(np.array_equal(eigval,eigval5)))
print('eigval1 == eigval2: %s' % str(np.array_equal(eigval1,eigval2)))
print('eigval1 == eigval3: %s' % str(np.array_equal(eigval1,eigval3)))
print('eigval1 == eigval4: %s' % str(np.array_equal(eigval1,eigval4)))
print('eigval1 == eigval5: %s' % str(np.array_equal(eigval1,eigval5)))
print('eigval2 == eigval3: %s' % str(np.array_equal(eigval2,eigval3)))
print('eigval2 == eigval4: %s' % str(np.array_equal(eigval2,eigval4)))
print('eigval2 == eigval5: %s' % str(np.array_equal(eigval2,eigval5)))
print('eigval3 == eigval4: %s' % str(np.array_equal(eigval3,eigval4)))
print('eigval3 == eigval5: %s' % str(np.array_equal(eigval3,eigval5)))
print('eigval4 == eigval5: %s' % str(np.array_equal(eigval4,eigval5)))
print('')
print('#'*50)

这是输出:

##################################################
L symmetric: True

L == L1 (before): True
L == L2 (before): True
L == L3 (before): True
L == L4 (before): True
L == L5 (before): True
L1 == L2 (before): True
L1 == L3 (before): True
L1 == L4 (before): True
L1 == L5 (before): True
L2 == L3 (before): True
L2 == L4 (before): True
L2 == L5 (before): True
L3 == L4 (before): True
L3 == L5 (before): True
L4 == L5 (before): True

L == L1 (after): True
L == L2 (after): True
L == L3 (after): True
L == L4 (after): True
L == L5 (after): True
L1 == L2 (after): True
L1 == L3 (after): True
L1 == L4 (after): True
L1 == L5 (after): True
L2 == L3 (after): True
L2 == L4 (after): True
L2 == L5 (after): True
L3 == L4 (after): True
L3 == L5 (after): True
L4 == L5 (after): True

U == U1: False
U == U2: False
U == U3: False
U == U4: False
U == U5: False
U1 == U2: False
U1 == U3: False
U1 == U4: False
U1 == U5: False
U2 == U3: True
U2 == U4: True
U2 == U5: True
U3 == U4: True
U3 == U5: True
U4 == U5: True

eigval == eigval1: True
eigval == eigval2: True
eigval == eigval3: True
eigval == eigval4: True
eigval == eigval5: True
eigval1 == eigval2: True
eigval1 == eigval3: True
eigval1 == eigval4: True
eigval1 == eigval5: True
eigval2 == eigval3: True
eigval2 == eigval4: True
eigval2 == eigval5: True
eigval3 == eigval4: True
eigval3 == eigval5: True
eigval4 == eigval5: True

##################################################

如何获得一致的、确定性的特征分解结果？

Answer 1

您对相同输入的浮点计算总是产生相同结果的期望实际上是错误的——即使在没有线程的单台计算机上也是如此。如果没有某些预防措施(这会影响性能)，在高性能计算中通常无法实现浮点可重复性，您在编写代码时需要考虑到这一点。

造成这种情况的原因有很多，其中之一就是优化编译器。例如，参见https://software.intel.com/sites/default/files/article/164389/fp-consistency-102511.pdf了解详情。